{
  "id": "1204.0107",
  "version": "v1",
  "published": "2012-03-31T15:33:15.000Z",
  "updated": "2012-03-31T15:33:15.000Z",
  "title": "Mean curvature flow of higher codimension in Riemannian manifolds",
  "authors": [
    "Kefeng Liu",
    "Hongwei Xu",
    "Entao Zhao"
  ],
  "comment": "28 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "We investigate the convergence of the mean curvature flow of arbitrary codimension in Riemannian manifolds with bounded geometry. We prove that if the initial submanifold satisfies a pinching condition, then along the mean curvature flow the submanifold contracts smoothly to a round point in finite time. As a consequence we obtain a differentiable sphere theorem for submanifolds in a Riemannian manifold.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-03-31T15:33:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "mean curvature flow",
      "riemannian manifold",
      "higher codimension",
      "initial submanifold satisfies",
      "arbitrary codimension"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1204.0107L"
    }
  }
}